The invention concerns a measuring configuration for NMR measurements, comprising a sample container that is closed on one side, wherein the material of the sample container has a magnetic susceptibility of χ2, an environment of a magnetic susceptibility of χ1, in which the sample container is arranged, and a sample substance which is contained in the sample container has a magnetic susceptibility of χ3, and takes up a volume within the sample container, wherein the volume of the sample substance consists of an upper partial volume, a lower partial volume and a center partial volume which comprises the origin of a spherical coordinate system with a z-axis, wherein the partial volumes adjoin one another, wherein the sample container has a first interface towards the environment and a second interface towards the sample substance, and, for certain designs of the sample container, the sample substance has a further interface between the sample substance and the environment, wherein there are magnetic susceptibility jumps at the interfaces, which cause location-dependent disturbance fields in the volume of the sample substance upon application of a predetermined external homogeneous magnetic field B0 which extends parallel to the z-axis, wherein the susceptibility jump at the second interface is sufficiently large that the maximum value of |B′G/B0| within the volume is at least 0.5 ppm, wherein, when a homogeneous magnetic field B0 has been applied, there is a first residual field in the center partial volume and a second residual field in the lower partial volume,
with
BG1: location-dependent z component of the magnetic field that is generated due to the susceptibility jump from χ1 to χ2 at the first interface G1;
BG2: location-dependent z component of the magnetic field that is generated due to the susceptibility jump from χ2 to χ3 at the second interface G2;
BG3: location-dependent z component of the magnetic field that is generated due to the susceptibility jump from χ3 to χ1 at the further interface G3;
F:=(B′G1+B′G2+B′G3)/B0: location-dependent relative field change due to the susceptibility jumps at the interfaces G1, G2, G3
B′j:=Bj−Bj: location-dependent deviation of the field Bj from the average value Bj
Bj: Average value of the z component of the field Bj, wherein (j=G1, G2, G3)
            R      1        :=                  (                              1                          V              1                                ⁢                                    ∫                              V                1                                      ⁢                                                            (                                      F                    -                                          F                      N                                                        )                                2                            ⁢                                                          ⁢                              ⅆ                V                                                    )                    1        /        2              ,first residual field (in the center partial volume (V1));
            R              2        ⁢        a              :=                  (                              1                          V                              2                ⁢                a                                              ⁢                                    ∫                              V                                  2                  ⁢                  a                                                      ⁢                                                            (                                      F                    -                                          F                      N                                                        )                                2                            ⁢                                                          ⁢                              ⅆ                V                                                    )                    1        /        2              ,second residual field (in the lower partial volume (V2a))
FN: Expansion of the relative field change F about the origin of the spherical coordinate system in rotationally symmetrical spherical functions up to order N, wherein N=4 to 10;
wherein the following applies in general:
      〈    A    〉    :=            1      V        ⁢                  ∫        V            ⁢                        A          ·                      ⅆ            V                          ⁢                  :                    Average value of any magnetic field A in the sample volume V;
      A    N    :=            ∑              n        =        0            N        ⁢                  a        n            ⁢                        K          n                ⁡                  (                      r            ,            θ                    )                    ⁢                          ⁢              :            
Expansion of A in rotationally symmetrical (i.e. independent of φ) spherical functions up to order N, with
an:=Expansion coefficients
Kn(r,θ)=rnPn(cos θ):=rotationally symmetrical spherical functions
Pn(cos θ):=Legendre polynomials
A measuring configuration of this type is disclosed in [6], [8].
NMR spectroscopy is a multifunctional tool for the chemical analysis of samples. Towards this end, a sample is disposed in a strong static magnetic field and subjected to electromagnetic pulses. The reaction of the nuclei in the sample is measured and analyzed. The properties of the static magnetic field influence the quality of the measurement results. The best results are generally obtained in a large magnetic field with high homogeneity. Field strengths of up to 23 T are used for high-resolution NMR spectroscopy. Superconducting magnets are used in this connection.
The typical measuring configuration that is used in modern spectrometers consists of a cylindrical superconducting coil that generates a strong magnetic field parallel to the axis in the cylindrical inner space. The cylindrical inner space also contains shim coils, gradients, and radio frequency coils, which are arranged in this inner space at different radii around a sample container. The sample container contains the substance to be examined. It must be made from an electrically insulating and chemically inert material.
The field homogeneity required for high-resolution NMR spectroscopy is of an order of magnitude of parts per billion (ppb). The superconducting magnet coil does generate a magnetic field that is sufficiently strong but is typically not sufficiently homogeneous. The magnetic field requires fine correction in order to obtain the required homogeneity. For this reason, the field homogeneity is normally corrected by means of a shim coil system. The shim coil system provides a number of coils with different geometrical arrangements. Currents in these coils generate magnetic fields in that region receiving the RF coils and the sample container. These magnetic fields are added to the magnetic field of the magnet. When the currents in the coils of the shim coil system are suitably adjusted, a largely homogeneous magnetic field can be obtained. Geometrical arrangements of shim coils in such shim coil systems are described e.g. in [1].
In addition to insufficient basic homogeneity of the magnet, all materials that are introduced into the magnetic field may cause a distortion of the magnetic field due to their magnetic susceptibility. These materials include, in particular, the RF coil and also the sample container and the sample substance itself. These magnetic field inhomogeneities may also be partially compensated for by magnetic fields of the shim coil system.
The process of adjusting the currents in the shim coil system with the aim to obtain as homogeneous a magnetic field as possible, is called shimming. There are different conventional shimming methods, e.g. [2], [3], [4]. All have in common that they receive signals from the sample substance with one of the RF coils during performance of the method, and determine the required current changes in the shim coils. For this reason, shimming takes into consideration only that volume portion of the sample substance that is in the sensitive area of the RF coil.
The coils of the shim coil system, which are rotationally symmetrical with respect to the magnet axis, play a particular role. They generate magnetic fields that are described by the rotationally symmetrical spherical functions.
They are required for shimming rotationally symmetrical field deviations.
The sample container may have different shapes in dependence on the application. A typical shape is a long rotationally symmetrical cylinder. There are two essential reasons for selecting a rotationally symmetrical cylindrical shape. Firstly, the cylindrical geometry generates magnetic disturbances, i.e. deterioration of the homogeneity of the static magnetic field (B0), only at the two ends. Secondly, rotationally symmetrical sample containers can be rotated during measurement and for this reason, one can average non-rotationally symmetrical field inhomogeneities with time. Their influence on the measurement result is thereby reduced.
In a configuration of this type, typically only half of the sample volume, namely the part located in the highly sensitive area of the radio frequency coil, substantially contributes to the measured signal. The additional sample substance is used to reduce the magnetic disturbances at the upper and lower borders of the sample volume. This additional sample substance has the following disadvantages: When there is only little sample substance available, the sample substance must be diluted to the required volume. This reduces, however, the measurement sensitivity in the highly sensitive area of the radio frequency coil.
The area of additional sample substance may also generate undesired NMR signals such as e.g. with respect to the problems of suppressing the solvent. The NMR signal of the substance to be examined (useful signal, e.g. of a protein) is often weaker by several orders of magnitude than that of the solvent (e.g. water). In this case, it is often not possible in terms of measurement technology to detect the weak signals in the presence of the undesirably strong solvent signal. The solvent signal can be suppressed by suitable pulse sequences. Since the solvent suppression in the upper and lower partial volumes is less efficient, solvent signals from these volumes may become considerably larger than the useful signal (NMR signal of the nuclei to be examined).
Both problems can be eased by reducing the magnetic disturbance of the ends of the sample container. Smaller magnetic disturbances allow the ends to be positioned closer to the highly sensitive area of the coil. This reduces, in turn, the region of additional sample substance. There are three conventional strategies for this reduction:
1. Adjustment of the magnetic susceptibility of the sample container to that of the sample substance;
2. selection of the interface towards the sample substance in the form of an ellipsoid of revolution;
3. selection of the two interfaces (exterior towards the sample container and sample container towards the sample substance) in such a fashion that the magnetic disturbances inside the sample substance largely cancel.
1. Adjustment of the Magnetic Susceptibility
When the susceptibility across the interface between the sample substance and the sample container remains constant, the magnetic field does not become inhomogeneous at that location. This configuration is described in [5], [6]. A sufficiently large amount of a paramagnetic substance is added to the material of the sample container, e.g. glass, in [6] such that the magnetic susceptibility of the container exactly corresponds to that of the sample substance to be examined. The outer interfaces are disposed remote from the sample volume for minimizing the magnetic disturbance in the sample volume due to the susceptibility change between the sample container and the exterior.
2. Interface in the Form of an Ellipsoid of revolution
One knows from [7] that the magnetic field inside a body, which has the interface of an ellipsoid and consists of magnetically homogeneous material, is homogeneous in the inside of the body when an external homogeneous magnetic field is applied. The magnetic susceptibility of the body (in the present case the sample substance container) may differ in this case from the magnetic susceptibility of the sample substance. Like in case of adjustment of the magnetic susceptibility, the end of the sample substance container remote from the sample substance must be sufficiently removed from the sample substance to ensure that the field inhomogeneity generated at this end does not have any influence on the sample volume.
3. Selection of the Two Interfaces in Order to Minimize the Field Inhomogeneity
In [8], the interface between the environment and the sample container and that between the sample container and the sample substance are selected in such a fashion that the magnetic field inside the sample volume remains largely homogeneous when a homogeneous magnetic field B0 is applied. The field disturbance inside the sample volume is therefore minimized through selection of the interfaces. No information is given about the type of disturbance that remains after selection of the interface prior to shimming with the exception that the field disturbances in the entire sample volume should be minimum.
The conventional devices, however, have considerable disadvantages.
In methods 1 and 2, the ends of the sample containers must be disposed remote from the central area in order to obtain the desired effect.
The technology for producing the glasses with susceptibility correction in accordance with method 2 is complex and expensive.
The sample bottoms generated according to method 3 are very thick. This is disadvantageous in that the sample is greatly extended and also becomes considerably heavier than a standard sample with a bottom having the same thickness as the sidewalls. Furthermore, in method 3, a residual field remains after shimming in all practical cases, i.e. in case of sample bottoms having a non-infinite thickness.
It is the object of the inventive device to obtain an NMR measuring configuration and a method for calculating the design of a sample container, thereby minimizing disturbances in an NMR measurement due to field inhomogeneities caused by susceptibility jumps at the interface between the sample container and the sample substance, and also minimizing the required volume of sample substance.